Phase sensitive detection

Applied to study of surface reactions

Felix Hemmingsson

CO2 conversion for energy storage

\[ \ce{CO2 + 4H2 -> CH4 + 2H2O} \]

\(\ce{Rh/CeO2}\) catalyst

  • high activity
  • high selectivity

Previous study

  • Material: Redox cycle
  • Same for surface reaction?

Figure: Change in diffraction pattern of \(\ce{Rh/CeO2}\) during \(\ce{H2}\) pulses. Catal. Sci. Technol., 2019, 9, 1644-1653

What kind of experiment is needed?

  1. Measure the reaction
    • In situ reaction system
    • High time resolution
    • Separate species
  1. Analyse the reaction
    • Separate active from stagnant
    • Reduce the noise
    • Sequence the reaction

The experimental setup

Had access to an in situ reaction chamber for FT-IR


DRIFTS
Diffuse Reflectance Infrared Fourier Transform Spectroscopy

… as well as mass flow controllers and rapid cross-over switch valves to build a gas system with

The analysis

Wanted to easily remove spectators and noise, and estimate a sequence of events.

Had heard of a technique called Phase sensitive detection…

Enhances a signal of a certain frequency (\(k\omega\)) and phase (\(\varphi\))

\[ A_k(\phi^\text{PSD}) = \frac{2}{T} \int^T_0 A(t)\sin (k\omega t + \phi_k^\text{PSD}) \mathrm{d}t \]

It is a cross-correlation

\[ A_k(\phi^\text{PSD}) = \frac{2}{T} \int^T_0 A(t)\sin (k\omega t + \phi_k^\text{PSD}) \mathrm{d}t \]

In essence, a cross-correlation between sampled data (\(f(t)\)) and modulating signal (\(g(t)\)). \[ (f*g)(\tau) := \int^{t_0+T}_{t0} \overline{f(t)} g(t + \tau) \mathrm{d}t \]

Phase sensitive detection

\[ A_k(\phi^\text{PSD}) = \frac{2}{T} \int^T_0 A(t)\sin (k\omega t + \phi_k^\text{PSD}) \mathrm{d}t \]

  • Remove stagnant components (cancelled by period)
  • Reduce noise (mismatching frequency)
  • Sequence the events (phase lags)
  • Improves time resolution (accumulate periods)

Showcasing the correlation


Figure: Animated illustration of a cross-correlation. Source: https://en.wikipedia.org/wiki/Cross-correlation


\[ A_k(\phi^\text{PSD}) = \frac{2}{T} \int^T_0 A(t)\sin (k\omega t + \phi_k^\text{PSD}) \mathrm{d}t \]

Simulated data

The cross-correlation

Lags in time:  (0.0, -29.0, 60.5, 30.0) s
Lags in phase: (0.0, -1.52, 3.17, 1.57) rad

Let’s look at an example (simulated)

We have the following reaction system (\(\ast\) is adsorption site)

\[ \begin{align} \ce{A (g) + \ast &-> A^\ast}\\ \ce{B (g) + \ast &-> A^\ast}\\ \ce{AB^{\ast} + B^\ast &-> AB2^{\ast} + \ast}\\ \ce{AB2^{\ast} + B^\ast &-> AB3^{\ast} + \ast}\\ \ce{AB3^\ast &-> AB3 (g) + \ast}\\ \end{align} \]

We will disturb the system by varying \(\ce{B (g)}\) as a sine

The simulated data

We measure the signals corresponding to the intermediates

The phase lags

The order: \(\varphi{(\ce{B^\ast})} < \varphi{(\ce{AB^\ast})} < \varphi{(\ce{AB2^\ast})} < \varphi{(\ce{AB3^\ast})}\)

Time for experiments!

But first, building time

  • Improve gas lines
  • Add pressure regulator
  • Update the software

Example data

Figure: Demodulated phase spectra (half period) of T = 60 s experiment. Catalysts 2020, 10(6), 601; https://doi.org/10.3390/catal10060601


As we want the lags (\(\varphi\)), we need to solve \(\phi_k^\text{PSD}\)

\[ A_k(\phi^\text{PSD}) = \frac{2}{T} \int^T_0 A(t)\sin (k\omega t + \phi_k^\text{PSD}) \mathrm{d}t \]

The composite plot

Figure: Demodulated phase spectra of T = 60 s experiment with maximum amplitude (line) for each individual wavenumber and some phase lags (dots). Catalysts 2020, 10(6), 601; https://doi.org/10.3390/catal10060601

  • \(\ce{CO3}\) or \(\ce{HCOO}\) “consumed” during \(\ce{H2}\) feed
  • Carbonyls (likely m-/b-/br-/h-\(\ce{CO}\)) are instead formed

What was the outcome?

I got:

  • to learn about instrumental setup and PSD
  • papers

Further developments on the system lead to:

  • automated (sequence programmed) FT-IR measurement
  • modularity of the instruments
  • prolonged measurement time

Old UI

New UI

Current setup

Thank you for your time!

<hfelix.se>